Given $ m \angle ABC = 9x + 47$, and $ m \angle CBD = 2x + 89$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Answer: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {9x + 47} + {2x + 89} = {180}$ Combine like terms: $ 11x + 136 = 180$ Subtract $136$ from both sides: $ 11x = 44$ Divide both sides by $11$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 2({4}) + 89$ Simplify: $ {m\angle CBD = 8 + 89}$ So ${m\angle CBD = 97}$.